Answer: The intensity of the sound produced by the vacuum cleaner is 1.28 x 10^(-3) W/m^2.
Explanation: The intensity (I) of a sound wave is given by:
I = 10^(L/10) * I0
where L is the sound level in decibels (dB) and I0 is the reference intensity, which is 1 x 10^(-12) W/m^2.
Substituting the given values, we get:
I = 10^(63.2/10) * 1 x 10^(-12)
I = 10^(6.32) * 1 x 10^(-12)
I = 1.28 x 10^(-3) W/m^2
Therefore, the intensity of the sound produced by the vacuum cleaner is 1.28 x 10^(-3) W/m^2.